Measuring the Deliquescence Point of Crystalline Sucrose as a Function of Temperature Using a New Automatic Isotherm Generator

Abstract

The relative humidity at which crystalline materials begin adsorbing large quantities of water from the atmosphere, termed the deliquescence point (RH_o), is an important temperature dependent stability parameter. The RH_o of a number of food and pharmaceutical materials has been determined at 25°C, but it is difficult to find RH_o values in the literature at other temperatures, even for common food materials, such as sucrose. Thus, the primary objective of this research was to assess the effect of temperature on RH_o for crystalline sucrose using a new automatic isotherm generator. A secondary objective was to determine and compare the RH_o value using three other methods (RH after the MC step change method, and two smoothing and second derivative methods [Savitzky-Golay and Yuan and others]), in addition to the commonly used linear extrapolation method. The AquaSorp DDI method provides an accurate, fast, and convenient means of measuring the initial real-time a_w values of the adsorption of water by the crystalline solid, making the DDI method an outstanding RH_o measuring method. A decrease in RH_o with increasing temperature was observed and attributed to increasing sucrose solubility with increasing temperature. No statistical difference (p = 0.05) was found between the four RH_o determination methods at each temperature, with the linear extrapolation method yielding RH_o values of 85.9, 85.7, and 84.0% at 15, 25, and 35°C, respectively.

Keywords:

• Sucrose
• Deliquescence
• Water activity
• Relative humidity
• AquaSorp isotherm generator

INTRODUCTION

Sucrose is widely used in the food industry because of the sweet taste and/or functional properties it contributes to food systems. Sucrose is one of the most common ingredients in foods and is important to the structure of many foods. For example, sucrose can either recrystallize or form an amorphous glass after baking, which affects the texture of baked products, such as cookies and biscuits.

Moisture sorption isotherms are useful for designing various food processes, such as dehydration,[1] and can be used to predict changes in food storage stability. Isotherms map the relationship between moisture content and water activity (a_w ). This moisture content-a_w relationship is complex and unique for each material due to the various interactions that can occur between the water and solid components at different moisture contents. In the case of crystalline sucrose, the isotherm exhibits a Type III or J-shaped isotherm. At a critical a_w or %RH value, the sucrose crystals begin to adsorb water from the atmosphere and dissolve. This critical %RH value is called the deliquescence point and is commonly termed the critical relative humidity (RH_o ) or the deliquescence relative humidity (DRH). RH_o is unique to each crystalline solid and is a function of temperature, where the temperature dependence follows the Clausius-Claperyron equation.[2]

Deliquescence is a first-order phase transition from solid to solution, induced by water uptake from the atmosphere and is depicted schematically in Figure 1. Figure 1, as well as the following description of the deliquescence process, is based on: Van Campen and others,[3] Zografi and Hancock,[4] Kontny and Zografi,[5] Hancock and Shambin,[6] Airaksinen,[7] Salameh and others,[8] Hiatt and others,[9] Newman and others,[10] Espinosa and others,[11] and Spackman and Schmidt.[12] At environmental relative humidity values (RH_E ) below the deliquescence point, water from the atmosphere is adsorbed at the crystalline solid surface, first forming a water monolayer, then at higher RH_E values forming multilayers (Fig. 1A). Upon increasing the RH_E to the critical relative humidity (RH_o ), the deliquescence process is initiated (Fig. 1B), that is, the solid starts to dissolve in the condensate film on the surface of the solid, forming, over time, a saturated solution (Fig. 1C), where RH_o is equal to the saturated solution a_w  × 100. The %RH at which deliquescence occurs (RH_o ) is a unique property of the crystalline solid and its storage temperature. If RH_E is increased further (Fig. 1D), the adsorption process continues until, over time, the vapor pressure of the solution becomes equal to the vapor pressure of the atmosphere (RH_E ), yielding a dilute (or undersaturated) solution, where the a_w  × 100 is equal to RH_E .

Figure 1 Schematic diagram of the interaction of a crystalline solid, such as sucrose, with water vapor in the atmosphere at various relative humility values, where RH_E = environmental relative humidity and RH_o = critical relative humidity. Stages A through D are explained in the text (color figure available online).

From a thermodynamic point of view, at each relative humidity, the crystalline sucrose can exist either as a solid or as an aqueous solution.[2] As depicted in Fig. 2, for %RH values lower than RH_o , the Gibbs free energy of the solid state is lower than the corresponding solution state. Therefore, the crystalline sucrose remains in the solid state. As the atmospheric %RH increases, the Gibbs free energy of the corresponding solution state decreases until it is equal to the Gibbs free energy of the solid state, which corresponds to the deliquescence point.

Figure 2 Gibbs free energy of a solid and its aqueous solution as a function of %RH. The %RH at which the solid and the solution Gibbs free energies become equal is the deliquescence point (DRH or RH_o ) (excerpted from reference 2).

Many common food and pharmaceutical materials are deliquescent. They are usually crystalline solids that are highly water soluble and can interact with water vapor from the atmosphere. Crystalline sugars, low-molecular-weight organic acids, inorganic salts, and vitamins, for example, thiamine HCl and sodium ascorbate, are deliquescent materials.[8] Salameh and Taylor[13] and Salameh and others[8] reported that the RH_o of a material is usually equal to the a_w of the corresponding saturated solution. Salameh and others[8] also reported that mixtures of deliquescent materials exhibited deliquescence lowering; that is, where the RH_o of two deliquescent materials is lower than the individual values of either deliquescent material. For example, a 50:50 mixture of crystalline sucrose, which has a RH_o of 85% at 25°C, and α-glucose monohydrate, which has a RH_o of 91% at 25°C, exhibited a lowered RH_o of 79% at 25°C.[8] Hiatt and others[9] indicated that the deliquescence phenomenon could increase the reactant mobility and chemical instability. Therefore, deliquescence may affect the shelf life, quality, functionality and packaging material prediction of food products that contain two or more deliquescent ingredients.

Knowledge of the RH_o of crystalline sucrose, a very a common deliquescent food material, as a function of temperature is very important for food product stability.[14,15] RH_o is often determined from a water sorption isotherm using the linear extrapolation method described by Salameh and Taylor,[13] where the %RH_o is determined by extrapolating the linear portions of the isotherm before and after the deliquescence event. Three additional methods of determining RH_o are explored in this article, a simple step change in moisture content method and two more calculation-intensive smoothing and second derivative methods.

The water sorption isotherm is traditionally generated by equilibrating the material of interest to select %RH (or a_w ) values over several saturated salt solutions.[16] Recently, automated water sorption instruments have been developed to overcome some of the limitations of the traditional saturated salt solution method.[17] Commercially available automatic water sorption instruments include, for example, the Dynamic Vapor Sorption instrument from Surface Measurement Systems Ltd., the IGAsorp from Hiden Analytical, the Cisorp Water Sorption Analyzer from C. I. Electronics Ltd., the Q5000SA and VTI Sorption Analyzer from TA Instruments, the AquaSorp from Decagon Devices Inc., the SPS–Moisture Sorption Analysis instrument from Projekt Messtechnik, and the Hydrosorb 1000 from Quantachrome.

The AquaSorp Isotherm Generator, employed in this study, utilizes the Dynamic Dewpoint Isotherm (DDI) method, which is unique among automatic isotherm generators. The DDI method directly measures a_w using a patented chilled-mirror dewpoint sensor, while it gravimetrically tracks weight change using a magnetic force balance. Thus, the sample is not equilibrated to a known (or selected) a_w value, but rather the a_w of the sample is measured throughout the real-time sorption process. Adsorption occurs as saturated wet air is passed over the sample, while desorption is accomplished as desiccated air is passed over the sample; both at a user selected flow rate. After roughly a 0.015 change in a_w , airflow is stopped and a snapshot of the sorption process is taken by directly measuring a_w and weight. The DDI method makes it possible to generate complete isotherms with 50 to 200 data points quickly (a few days) and accurately without long equilibration times. However, as pointed out by the manufacturer, in some cases (e.g., materials with slow diffusion rates) the DDI method may not yield an isotherm comparable to the traditional equilibrium-based isotherm.[17,18]

Moisture sorption isotherms, and thus the deliquescence point, vary with temperature.[2,19,20] In general, the deliquescence point of sugars and salts decreases as temperature increases, due to increasing solubility of these materials with increasing temperature. This solubility temperature dependence can be observed in Table 1 for sucrose, where the solubility of sucrose increases from 1.9443 g sucrose/g water at 15°C to 2.2435 g sucrose/g water at 35°C. Isotherms of crystalline sucrose are available in the literature, but most isotherms were obtained near room temperature, 20 or 25°C.[21–23 23 Audu and others[24] studied sucrose isotherms at 80°C using a dynamic method (details of the nature of the dynamic method, however, were not specified). Thus, the main objective of this study was to determine the deliquescence point of crystalline sucrose as a function of temperature, 15, 25, and 35°C, using the new isotherm AquaSorp isotherm generator. The secondary objective of this study was to determine and compare the RH_o value using three other methods (RH after the MC step change method, and two smoothing and second derivative methods [Savitzky-Golay and Yuan and others]), in addition to the commonly used linear extrapolation method.

Table 1 Saturation solubility data for sucrose in water in both g sucrose per g water and %MC (dry basis) units as a function of temperature from Bubník and Kadlec.[28]

Temperature (°C)	Sucrose (g) per water (g)	%MC (db)
15	1.9443	51.432
20	2.0047	49.883
25	2.0741	48.214
30	2.1535	46.436
35	2.2435	44.573

MATERIALS AND METHODS

Materials

Crystalline sucrose, ACS reagent grade (Sigma-Aldrich Co., St. Louis, MO) was used “as is.” The particle size was measured using USA standard testing sieves (W.S. Tyler, Mentor, OH, USA). All sucrose particles were greater than 300 μm and 98.2% were greater than 425 μm. The moisture content of the “as is” crystalline sucrose, determined using Karl Fisher titration, was 0.004% on a wet basis. Deionized water was used to prepare the saturated sucrose solutions.

Methods

Dynamic dewpoint isotherms

Crystalline sucrose dynamic dewpoint isotherms (DDI) were generated using the AquaSorp isotherm generator (Decagon Devices, Inc., Pullman, WA, USA) at 15, 25, and 35°C. Approximately 600 mg of crystalline sucrose was loaded into a sample cup and placed on the precision balance. In general, a minimum amount of sample, just enough to cover the bottom of sample cup, was used to decrease the experimental time and, as will be discussed in the Results and Discussion section, to minimize the diffusion-associated increases in a_w after the deliquescence point. However, for one run at 15°C, 2300 mg of crystalline sucrose was used, but exhibited no difference in the deliquescence point obtained. During the experiment, the sample was exposed to increasing %RH values via exposure to water saturated air at a user selected 300 mL/min flow rate. The ending %RH was approximately 90% (or 0.90 a_w ). During the experiment, a_w and weight data were collected. After the isotherm was complete, the weight data were converted to moisture content (dry basis) using the initial moisture content of the crystalline sucrose.

RH_o determination

RH_o is commonly determined by calculating the intersection of the extrapolated linear portions of the isotherm before and after the deliquescence event (termed the linear extrapolation method). The criteria used to distinguish the data to be used in the extrapolation method were as follows. The first large gap in the moisture content data, calculated as the difference between two sequential moisture content points, was used to separate the isotherm into two sections: before and after the deliquescence event. A change in a_w greater than ±0.005 (the reported AquaSorp accuracy) was used to determine which isotherm data points to exclude in the extrapolation for the linear portion after the deliquescence event. A low R ² is often associated with the linear portion after the deliquescence event due to the nearly vertical increase in moisture content with nearly no change in a_w ; however, the low value of R ² did not affect the use of the linear equation for determining RH_o .

Three additional methods were used to determine RH_o : (1) the first RH value after the beginning of the deliquescence event, determined by the first large increase in the moisture content data, calculated as the difference between two sequential moisture content points (termed the RH after the MC step change method) was identified as the RH_o value; (2) an Excel spreadsheet algorithm based on the Savitzky-Golay smoothing and differentiation method[25] (assumes equally spaced a_w data) developed by Decagon Devices Inc. (Pullman, WA, USA) (termed the Savitzky-Golay method); and (3) the relative humidity value where the moisture content changed most dramatically, determined by smoothing the isotherm data and taking the second derivative of the fitted isotherm curve using the MATLAB program (The MathWorks, Inc., Natick, MA, USA). The procedures used to obtain the second derivative were as follows. The water activity (a_w ) and moisture content (% db) data were smoothed using loess (local polynomial regression fitting) smoothing (second degree polynomial) with a span of 11 points. Next, the smoothed data set was fit using a smoothing cubic spline, after which the first derivative of the fit was taken. Using the data from the first derivative as the new data set, the above smoothing and fitting procedures were repeated, after which the first derivative of the fit was again taken, evaluated at every 0.001 unit (to optimize peak location), resulting in the second derivative. The maximum of the second derivative curve, in the targeted region, is the critical relative humidity (RH_o ) value. The procedure was developed by Yuan and others[26] (termed herein the Yuan and others method). The major difference between the Savitzky and Golay and Yuan and others methods is that the Yuan and others method does not assume equally spaced a_w data. A detailed discussion comparing the Savitzky-Golay and the Yuan and others methods is given in Yuan.[27]

Saturated Sucrose Solution Preparation

Saturated sucrose solutions were prepared by adding sucrose to deionized water. The beaker was covered with parafilm. To ensure that the sucrose solutions would be saturated, 90 g of sucrose was added to 40 g of water at room temperature and stirred using a magnet stir bar on a stir plate for 24 h to ensure complete dissolution of all the sucrose that could dissolve. Excess sucrose crystals remained at the bottom of the beaker. The initial amount of sucrose used was based on the sucrose solubility data of Bubník and Kadlec[28] at 35°C (Table 1). Aliquots of 10 mL were then taken and transferred into AquaLab sample cups and placed overnight (16 h) on a temperature control plate (Decagon Devices Inc., Pullman, WA, USA) set at the desired temperature, 15, 25, or 35°C. The sample cups were covered with lids. The sample was stirred with a glass stir rod several times during the temperature control period. The a_w of the solutions was then measured three times using an Aqua Lab Series 4TE meter (Decagon Devices Inc., Pullman WA, USA). The entire sample preparation procedure was repeated three times at each temperature.

Water Activity Measurements

Saturated sucrose solution was prepared in triplicate and the a_w value was measured in triplicate (for a total of nine a_w measurements per temperature) at 15, 25, and 35°C using an Aqua Lab Series 4TE a_w meter (Decagon Devices, Inc., Pullman, WA, USA). To ensure complete temperature and vapor equilibration, the a_w values were taken after 1 h of continuous a_w measurements.

Statistical Analysis

A one-way between-group analysis of variance was conducted to determine whether there was a significant difference among the RH_o values obtained by the four methods and the saturated solution a_w  × 100 at each temperature. A least significant difference test was used to determine the location of the difference. The level of significance was set at p = 0.05.

RESULTS AND DISCUSSION

DDIs for crystalline sucrose at 15, 25, and 35°C, as well as the measured saturated sucrose a_w values, are shown in Figure 3. Since each DDI run is unique, average isotherm values cannot be calculated; rather, duplicate runs were plotted for each temperature so variation in the isotherms could be visually assessed. As expected, crystalline sucrose, at all three temperatures, exhibited typical type III isotherm behavior—little moisture adsorption at low a_w values followed by a dramatic rise in moisture content after the deliquescence point, RH_o . At RH_o , the solid particle spontaneously adsorbs water from the atmosphere, producing a saturated solution.[2] Further increase in the atmospheric %RH leads to additional water adsorption by the sucrose solution to maintain thermodynamic equilibrium. If the atmospheric %RH decreases, evaporation of water will occur. However, it is interesting to note that the solution typically does not recrystallize at the RH_o , but remains supersaturated until a much lower %RH, at which recrystallization occurs.[2]

Figure 3 Crystalline sucrose DDIs obtained using a 300 mL/min flow rate and saturated sucrose solution values (moisture content values from Table 1 and a_w values from this study [Table 2]) at 15, 25, and 35°C.

Theoretically, the a_w of the saturated solutions should remain constant until all of the sucrose completely dissolves. However, as shown in Figure 3, a_w values after the deliquescence event do not remain constant until all of the sucrose completely dissolves, but rather begin to slowly increase. This increase in a_w values before achieving the saturated solubility a_w value is attributed to slow diffusion of the adsorbing water and dissolving sucrose, setting up an a_w gradient from the atmosphere-solution interface (slightly higher a_w ) to the dissolving crystalline sucrose interface (saturated solution a_w ). It takes time for the water and dissolving sucrose to completely mix. However, before complete mixing can be achieved, the next set of weight change and a_w measurements are being taken by the AquaSorp instrument. In order to minimize the effects of the diffusion process, a minimum amount of sample should be used and a reasonably slow AquaSorp flow rate selected. This slow diffusion problem explains why some of the a_w data after the deliquescence point and before the saturated solubility point could not be included in the linear extrapolation calculation. It is important to point out that the increase in a_w values before achieving the saturated solubility a_w value observed in Figure 3, does not interfere with obtaining accurate RH_o values. Rather, being able to measure the initial real-time a_w values (the real-time response to water adsorption by the crystalline solid), instead of equilibrium a_w values, makes the DDI method an outstanding RH_o measuring method.

RH_o values obtained via four different methods at 15, 25, and 35°C are given in Table 2. In addition, a_w and RH_o values found in the literature are included in Table 2 for comparison purposes. There was no statistical difference between the four methods of obtaining the RH_o values at any of the three temperatures (Table 2). This result indicates that all four methods can be used to obtain the RH_o values from the DDI method. The Linear Extrapolation and the RH after the MC Step Change are the simplest methods and, based on the results reported herein, generate the same RH_o values as the more calculation intensive second derivative methods (Savitzky-Golay and Yuan and others).

Table 2 Saturated sucrose solution a _w and deliquescence point (RH _o ) values of crystalline sucrose at 15, 25, and 35°C

		RHo values for four methods				Literature values
Temp. (°C)	aw  × 100	Linear extrapolation	RH after the MC step change	Savitzky-Golay	Yuan and others	aw  × 100	RHo	References
15	86.2 ± 0.20^a	85.9 ± 0.40^a	86.3 ± 0.10^a	86.3 ± 0.00^a	86.3 ± 0.20^a
25	84.8 ± 0.80^a	85.7 ± 0.10^a	85.8 ± 0.00^a	85.6 ± 0.07^a	85.9 ± 0.10^a	85.0	85.0	Salameh and others[8]
						84.3		Van Campen and others[29]
							84.4	Rüegg and Blanc[30]
35	84.4 ± 0.20^a	84.0 ± 0.10^b	84.0 ± 0.10^b	84.0 ± 0.07^b	84.0 ± 0.10^b
The RHo values were obtained using four different methods as explained in the Materials and Methods section.
Means with the same letter within a row (difference among measurement methods and the saturated solution aw at a given temperature) are not significantly different at p = 0.05.

The statistical results in Table 2 also show the comparison between the three RH_o values and the saturated solution a_w values at each temperature. At 15 and 25°C, there was no statistical difference between the RH_o values and the saturated solution a_w  × 100 values; however, at 35°C a statistical difference was observed between the three RH_o values and the saturated solution a_w . Theoretically, at a given temperature, the saturated solution a_w  × 100 value should be equal to the RH_o value.[2,3,31] Thus, the statistical difference observed for 35°C may be attributed to the very small amount of variation obtained for the RH_o values at that temperature. It should be pointed out that even though there is a statistical difference between the RH_o values and the saturated solution a_w at 35°C, there is no practical difference.

As predicted by theory and exhibited by the experimental values in Table 2, for sucrose both the RH_o values and the saturated solution a_w values decreased with increasing temperature.[2,32,33] This result can be attributed to the increasing solubility of sucrose at higher temperatures (Table 1). The decrease in the deliquescence point with temperature for sucrose can be calculated using the following equation derived from the Clausius-Clapeyron equation as shown in Seinfeld and Pandis[2]:

(1)

where n is the solubility of the solute in water (moles of solute per mole of water) (calculated based on Table 1), ΔH_s is the enthalpy of solution, R is the gas constant (8.314 J/K·mol), and T is the temperature (in K). After integration, the RH_o value for crystalline sucrose can be calculated using Eq. (2):

(2)

where T ₀ > T. The details of the derivation of Eq. (2) are given in Wexler and Seinfeld.[34] Two assumptions underlie the use of Eq. (2)—both the enthalpy of solution (ΔH_s ) and the solubility (n) are constant over the temperature range of interest. Using a literature obtained value of 6430 J/mol[34] for (ΔH_s ) and the DDI Linear Extrapolation RH_o value at 25°C, RH_o values at 15 and 35°C were calculated using Eq. (2) (Table 3). Calculated and Linear Extrapolation RH_o values were similar and both followed the trend of decreasing RH_o with increasing temperature. Equation (2) was also used to calculate the enthalpy of solution (ΔH_s ), using the experimental RH_o values at 15 and 35°C and the molar solubility of sucrose (n in Table 3) at 25°C (represents an average sucrose concentration value). The calculated ΔH_s value was 7555.6 J/mol, which is reasonably close to the value of 6430 J/mol obtained from the literature.

Table 3 Calculated RH_o values at 15 and 35°C using Eq. (2) compared to extrapolated RH_o values (Table 2). The solubility of sucrose in mol/mol (n) was calculated using the solubility data in Table 1

Temperature (°C)	Solubility of sucrose, n (mol/mol)	Linear extrapolation RHo	Calculated RHo
15	0.10233	85.9	86.5
25	0.10916	85.7 ^a	—
35	0.11334	84.0	84.9
^aValue used to calculate RHo values at 15 and 35°C.

CONCLUSIONS

The deliquescence point (RH_o ) of crystalline sucrose was determined using a new automatic isotherm generator at 15, 25, and 35°C. The DDI method provides an accurate, fast, and convenient means of measuring the initial real-time a_w values of the adsorption of water by the crystalline solid, making the DDI method an outstanding RH_o measuring method. Four different methods, Linear Extrapolation, RH after the MC Step Change, and two smoothing and second derivative methods [Savitzky-Golay and Yuan and others methods]), were used to obtain the RH_o values from the isotherms. The RH_o values from the four methods were found to be statically equivalent at p = 0.05. As predicted from theory, RH_o decreased as the temperature increased.

ACKNOWLEDGMENTS

The authors would like to acknowledge the support of Kraft Foods for their contribution to the joint Undergraduate and Masters Program between the University of Illinois, Urbana-Champaign, IL and China Agricultural University, Beijing, China. The use of the AquaSorp instrument from Decagon Devices Inc. (Pullman, WA) is also gratefully acknowledged.

Notes